Possibilistic Instrumental Variable Regression

TL;DR

This paper introduces a possibilistic approach to instrumental variable regression that enables causal inference and sensitivity analysis even with potentially invalid instruments, using possibility theory for posterior inference.

Contribution

It presents a novel possibilistic method for instrumental variable regression that handles invalid instruments and performs sensitivity analysis, which was not addressed in prior work.

Findings

Strong performance in simulations

Effective sensitivity analysis with invalid instruments

Applicable to real-world data scenarios

Abstract

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the exogeneity assumption. Our method can provide informative results even when only a single, potentially invalid, instrument is available, offering a natural and principled framework for sensitivity analysis. Simulation experiments and a real-data application indicate strong performance of the proposed approach.